There are a number of theoretical and practical reasons to adopt the Bayesian framework over classical techniques. Recently, many psychological models have benefited from Bayesian analyses, and in particular, they have benefited from hierarchical analyses that provide information on multiple levels. However, the class of models that are capable of enjoying the benefits of Bayesian analyses has been limited to models that possess tractable likelihood functions. These models are typically referred to as simulation-based models, and as a result of their complicated or intractable likelihood functions, Bayesian analyses are not possible. However, a new technique, called approximate Bayesian computation (ABC), allows researchers to circumvent the evaluation of the likelihood by simulating the model. Our proposed research will extend the application of ABC to complex, stochastic models of computational neuroscience. For these models, we will be interested in fitting hierarchical and finite mixture versions of the models to examine individual differences and explore the role of experimental design optimization in model selection. PUBLIC HEALTH RELEVANCE: The analysis of stochastic complex models of computational neuroscience will advance our understanding of the underlying mechanisms in the cognitive system guiding the behavior of interest. Introducing the general framework for Bayesian likelihood-free inference will have a broad impact on any field employing computational models. This will be of particular interest in computational neuroscience where models of human behavior are often very sophisticated and have complex likelihood functions.